11) The wave function of a many-electron closed-shell atom can be expressed as a Slater determinant....

11) The wave function of a many-electron closed-shell atom can be expressed as a Slater determinant. A useful property of determinants is that interchanging any two rows or columns changes their sign and therefore that if any two rows or columns are identical, then the determinant vanishes.

Use this property to show that (a) no two electrons can occupy the same orbital with the same spin.

Expert Solution

The wavefunction of 2 electron system in obritals and where both the electrons have same spin is given by

where r1 and r2 are coordinates of the two electrons.

When the orbitals are the same, the wave function becomes

This determinant is zero because both the columns of the determinant are the same and therefore the wave function of the 2 electron system is zero.

Hence two electrons cannot occupy the same orbital with the same spin.

genius_generous answered 2 years ago

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